building a network with time machines

I have large area to cover and am wanting to use my 3 TC for an extended network.
So far no problem. Questions
1. do I use static IP for TC at the modem and "join" the other 2 TC's or DCHP all
I seem to get some issues when all are in DCHP and I have no idea why?
2. I have a wired network with a switch also, Switch is directly connected to modem with most hardwires ports after that switch BUT my 3 TC are connected directly to modern and not switch, see any issue with this?

You're getting issues when all three are issuing IP addresses by DCHP because unless you limit the range to prevent overlaps you'll get clashes.
A single router (TC1 in my suggested config) should act as the DCHP server for the entire network.

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What is it you're trying to do exactly?
When you say 'extend the network' I assumed you meant wireless because if you are able to use cable then just use cable. Which kind of makes TC2 and 3 redundant. Perhaps if you could give a few more details of what equipment you're connecting and how you want it connected.

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Ok I will try to explain
I have the main internet come to a closet upstairs, I have Cat 5 to all rooms from their. I am connecting all of those to switch that is getting it's internet feed from the TC 1 as you suggested. My desire for Wifi to be extended is that many of the divides we now have are not ethernet compadible. So I thought I would create a wireless "hotspot" with the additional 2 TRC's. This way there is only one wireless network to join from any point in the home.Plus I can use the Time machines for various computer backup areas.

Is it better to just plug in the TC's 2 and 3 into the ethernet that is coming in after the switch and if I do this is it still broadcasting just one wireless network.